Back to theory,
in a nutshell the tunneling-currents approach requires to abandon the widespread
view of amorphous solids as continuously- and homogeneously-disordered media at
the atomic and MR scale (the CRN model, which continues to represent a useful
zero-order approximation).
Instead, one admits that – for a bulk glass – the DH scenario characterizing the
supercooled liquid state [1]} continues to be valid below \(T_g\) .
Here, the “amorphous” solid state is made up of solid-like particle regions –
jammed together below \(T_g\)  – and liquid-like particle regions in between
[2]}. The solid-like regions are also known to be better-ordered as well
[3]}, [4]}, [5]}, at least there is strong evidence just above
\(T_g\)  [6]}, [7]}, hence they are called RER (regions of enhanced
regularity) in the glass. The particles that are more mobile – also those proximal
to RER walls, which are most likely charged O\(^-\)  dangling bonds for the
multi-silicate glasses – get to be squeezed together in the “voids” between
the solid-like RER which themselves make up a close-packed true random solid.
These charged, mobile particles in the “voids” will be highly correlated and
subjected to complicated forces from their surroundings. A reasonable hypothesis
[8]}, [9]} is that they will tunnel coherently as effective
quasi-particles in each highly-correlated void-contained “liquid drop”, the
effective “particles” having large negative effective charge \(Q\) , \(|Q|\gg |e|\) 
(\(e\)  is the electron's charge) and heavily renormalized tunneling parameters
[8]}, [9]}. Each tetrahedral void between mostly four RER being
composed of four faces, the quasi-particles – one for each face
– will be subjected to an effective local potential having three-fold topology
(or symmetry, for perfect RER local tetrahedral arrangement, then becoming a
distorted three-welled tunneling potential with topological disorder in the shape,
size and final location of the four RER). These quasi-particles are the sources
of orbital magnetic moments (having a collective local nature) and are believed
[12]} to be the sources of the observed intrinsic “glass-magnetisation”
\(M_{intr}^{tunn}\) . More about this model of glasses in the SI and in
[2]}, [14]}.
